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Elasticity

- What do you think?
- Could reducing the supply of illegal drugs cause an increase in drug-related burglaries?

Chapter 4: Elasticity

S $2500 = $50 x 50

Sâ€™ $3200 = $80 x 40

Sâ€™

80

S

50

D

40

50

e.g. 4.1 The Effect of Extra Border Patrols on the Market for DrugsHow will drug addicts behave?

P($/ounce)

Q(1,000s of ounces/day)

Chapter 4: Elasticity

Price Elasticity of Demand

- is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good.
- i.e. the percentage change in the quantity demanded that results from a 1 percent change in its price.

Chapter 4: Elasticity

Example 4.2

- The price of beef increases by 2% and the quantity demanded decreases by 6%
- Then the price elasticity of demand for beef is

- 6%

-3

=

2%

Chapter 4: Elasticity

Price Elasticity of Demand

- Measuring Price Elasticity of Demand

- Observations
- Price elasticity of demand will always be negative (i.e., an inverse relationship between price and quantity).
- For convenience sometimes we drop the negative sign/ take absolute sign.

Chapter 4: Elasticity

Price Elasticity of Demand

Unit elastic

inelastic

Elastic

Price elasticity

of demand

-3

-2

-1

0

Chapter 4: Elasticity

e.g 4.3elasticity of demand for dim sum?

- Originally
- Price = $10/piece
- Quantity demanded = 600 pieces/day

- New
- Price = $9.5/piece
- Quantity demanded = 606 pieces/day, then

-1

(606 - 600)/600

1%

=

=

(9.5 - 10)/10

-5%

5

Inelastic!

Chapter 4: Elasticity

Example 4.4 What is the elasticity of Ocean Park Annual Passes?

- Originally
- Price = $1200
- Quantity demanded = 20,000 passes/year

- New
- Price = $1140
- Quantity demanded = 26,000 passes/year, then

(26000 - 20000)/20000

30%

=

=

-6

(1140 - 1200)/1200

-5%

Elastic!

Chapter 4: Elasticity

Determinants of Price Elasticity of Demand

- Availability of substitutes
More substitute to choose from

ïƒ when P of good X changesïƒ people can substitute X by other goods easily

ïƒ higher elasticity

Chapter 4: Elasticity

Determinants of Price Elasticity of Demand

- Proportion of income used to buy the good
ïƒ the higher the fraction of income spent on a good x

ïƒ higher elasticity as a slight increase in Px will affect your purchasing power adversely

ïƒ e.g. Housing

Chapter 4: Elasticity

Determinants of Price Elasticity of Demand

- Temporary versus permanent change in price
ïƒ if price change is temporary

ïƒ people react more to it

ïƒ higher elasticity

ïƒ e.g. Airline promotions

Chapter 4: Elasticity

Determinants of Price Elasticity of Demand

- Time
ïƒ facing a sudden price increases

ïƒ if we have more time to search for substitutes

ïƒ responsiveness higher

ïƒ higher elasticity

ïƒ e.g. marketing tactics

Chapter 4: Elasticity

e.g 4.5 Price Elasticity Estimates for Selected Products

Good or service Price elasticity

Green peas -2.80

Restaurant meals -1.63

Automobiles -1.35

Electricity -1.20

Beer -1.19

Movies -0.87

Air travel (foreign) -0.77

Shoes -0.70

Coffee -0.25

Theater, opera -0.18

Why is the price elasticity of demand more than 14 times larger for green peas than for theater and opera performances?

Chapter 4: Elasticity

A Graphical Interpretationof Price Elasticity

- For small changes in price

Where Q is the original quantity and P is the original price.

Chapter 4: Elasticity

P

P

P - P

Q

D

Q

Q + Q

A Graphical Interpretationof Price Elasticity- For small changes in price

Price

Chapter 4: Elasticity

A

Example 4.6 Calculating Price Elasticity of Demand20

16

12

Price

8

Question:

What is the price elasticity

of demand when P = $8?

4

1

2

3

4

5

Quantity

Chapter 4: Elasticity

D1

6

4

D2

4

6

12

Example 4.7 Price Elasticity and Steepness of the Demand CurveWhat is the price elasticity of Demand for D1 & D2 when P = $4?

P

Observation

If two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point.

Q

Chapter 4: Elasticity

a/2

b/2

b

Price Elasticity Regions along a Straight-Line Demand CurveObservation

Price elasticity varies at every point along a straight-line demand curve

Price

Quantity

Chapter 4: Elasticity

Example 4.8 Price Elasticity Regions along a Straight-Line Demand Curve

When P = $4

When P = $1

12

6

Price

Observation

Price elasticity varies at every point along a straight-line demand curve

4

D

1

4

6

10

12

Quantity

Chapter 4: Elasticity

Quantity

Perfectly Elastic Demand CurveIf the price increases a little, the quantity demanded will drop to zero. If the price drops a little, the quantity demanded will increase a lot.

i.e. Consumers are extremely responsive to price changes

Chapter 4: Elasticity

Quantity

Perfectly Inelastic Demand CurveThe quantity demanded is not responsive to any change in price.

i.e. consumers are extremely inert to changes in price

Chapter 4: Elasticity

Elasticity & Total Expenditure

- From a consumerâ€™s point of view,
- Total Expenditure = P x Q
- Market demand measures the quantity (Q) at each price (P)

- Total Expenditure = Total Revenue
(buyerâ€™s view) (sellerâ€™s view)

Chapter 4: Elasticity

10

8

6

Price ($/ticket)

4

2

0

1

2

3

4

5

6

Quantity (100s of tickets/day)

Example 4.9 The Demand Curve for Drama TicketsPrice ($/ticket)

Total expenditure ($/day)

12

0

10

1000

8

1600

ïƒŸ HIGHEST!

6

1800

4

1600

2

1000

0

0

Chapter 4: Elasticity

10

1,800

1,600

8

6

Price ($/ticket)

1,000

Total expenditure ($/day)

4

2

0

2

4

6

8

10

12

0

1

2

3

4

5

6

Price ($/ticket)

Quantity (100s of tickets/day)

Total Expenditure as a Function of PriceTotal revenue is at a maximum at the midpoint on a straight-line demand curve.

Chapter 4: Elasticity

Example 4.10

- What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd?

- When P drop
- Total Exp rise (fall)
if gain from additional sales is larger (smaller) than loss from existing sales

Chapter 4: Elasticity

Example 4.11 Elasticity and Total Expenditure

- Should a jazz band raise or lower its price to increase total revenue?
- Assume P=$20, Q=5,000, and e=-3.

- Total revenue = $20 x 5,000 = $100,000/week
- If P is increased 10%,
- Q will decrease 30%
- Total revenue = $22 x 3,500 = $77,000/week

- If P is lowered 10%,
- Q will increase 30%
- Total revenue = $18 x 6,500 = $177,000/week

Assume: Production Cost data is negligible in this case.

Chapter 4: Elasticity

Elasticity and the Effect of a Price Change on Total Expenditure

Chapter 4: Elasticity

Unitarily elastic demand curve Expenditure

P

Unitary elastic: PxQ=constant

ïƒ all P, Q combinations yield

the same TR for seller

ïƒ elasticity on all points= 1

Q

Chapter 4: Elasticity

e.g. 4.12: should bus fare increases? Expenditure

- A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that:
a. a fare increase will increase total revenue.

b. demand for bus service will go up as fares increase.

c. demand is price elastic.

d. a 10 percent fare hike will produce a 20 percent reduction in riders.

e. the price elasticity is -5.

Chapter 4: Elasticity

e.g. 4.12: should bus fare increases? Expenditure

- A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that:

- We are told that when DP/P = 1%, DQ/Q = -0.2%.
- Elasticity = (DQ/Q)/(DP/P) = -0.2. (inelastic)
So a fare increase will increase total revenue.

Chapter 4: Elasticity

e.g. 4.12: should bus fare increases? Expenditure

- A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that:
a. a fare increase will increase total revenue.

b. demand for bus service will go up as fares increase.

c. demand is price elastic.

d. a 10 percent fare hike will produce a 20 percent reduction in riders.

e. the price elasticity is -5.

answer a is correct.

Chapter 4: Elasticity

Cross-Price Elasticity of Demand Expenditure

- The percentage by which quantity demanded of the good X changes in response to a 1 percent change in the price of the good Y
- Substitute Goods
- Complement Goods

Chapter 4: Elasticity

Cross-Price Elasticity of Demand Expenditure

Substitute Goods

- the cross-price elasticity of demand is positive
- â€˜positiveâ€™ = move in same direction
- When Px â†‘(â†“) ïƒ Qy â†‘(â†“)
- E.g. Coffee & Tea
Complement Goods

- the cross-price elasticity of demand is negative
- â€˜negativeâ€™ = move in opposite direction
- When Px â†“ (â†‘) ïƒ Qy â†‘(â†“)
- E.g. Coffee & Cream

Chapter 4: Elasticity

Income Elasticity of Demand Expenditure

- The percentage by which quantity demanded changes in response to a 1 percent change in income
- Normal Goods
- Inferior Goods

Chapter 4: Elasticity

Income Elasticity of Demand Expenditure

- Normal Goods
- Income elasticity is positive
- Income â†‘(â†“) ïƒ Qx â†‘(â†“)
- E.g. income and movie

- Inferior Goods
- Income elasticity is negative
- Income â†“ (â†‘) ïƒ Qx â†‘(â†“)
- E.g. income and McDonalds
(letâ€™s assume youâ€™re not a big fanâ€¦)

Chapter 4: Elasticity

Now, the Supply Side Expenditure

So much for Demand side, let us change to the supply side discussion for elasticities

Chapter 4: Elasticity

The Price Elasticity of Supply Expenditure

- Price Elasticity of Supply
- The percentage change in the quantity supplied that occurs in response to a 1 percent change in price

Chapter 4: Elasticity

S Expenditure

A

8

4

2

e.g. 4.13 A Supply Curve for Which Price Elasticity Declines as Quantity RisesB

10

8

- Observations:
- Elasticity >0
- Elasticity >1 for linear supply curve that has a positive Y-intercept.
- Elasticity decreases as quantity increases.

Price

0

2

3

Quantity

Chapter 4: Elasticity

S Expenditure

B

5

A

4

P

Q

Price

0

12

15

Quantity

e.g. 4.14 A Supply Curve for Which Price Elasticity is unityThe price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin.

Chapter 4: Elasticity

S Expenditure

Elasticity = 0 at every

point along a vertical

supply curve

Perfectly Inelastic Supply CurveWhat is the price elasticity of supply of land within Central?

Price ($/acre)

0

Quantity of land in Central

(1,000s of acres)

Chapter 4: Elasticity

If Marginal Cost of production is constant, then the Expenditure

price elasticity of supply at every point

along a horizontal supply curve is infinite

ïƒ More on Chapter 6

S

A Perfectly Elastic Supply CurvePrice (cents/cup)

14

0

Quantity of lemonade

(cups/day)

Chapter 4: Elasticity

Determinants of Supply Elasticity Expenditure

- Flexibility of inputs
- Mobility of inputs
- Ability to produce substitute inputs
- Time

Chapter 4: Elasticity

e.g.4:15 Expendituregasoline prices vs car prices

- Why are gasoline prices so much more volatile than car prices?
- Differences in markets
- Demand for gasoline is more inelastic
- Gasoline market has larger and more frequent supply shifts

Chapter 4: Elasticity

Sâ€™ Expenditure

S

1.69

1.02

D

7.2

6

e.g.4:15 gasoline prices vs car pricesGasoline

Greater Volatility in Gasoline Prices than in Car Prices

Price ($/gallon)

0

Quantity

(millions of gallons/day)

Chapter 4: Elasticity

Sâ€™ Expenditure

S

17

16.4

D

11

12

e.g.4:15 gasoline prices vs car pricesGreater Volatility in Gasoline Prices than in Car Prices

Cars

Price ($1,000s/car)

Quantity

(1,000s of cars/day)

Cars

Chapter 4: Elasticity

e.g.4:15 Expendituregasoline prices vs car prices

- Conclusion:
- Price will be more volatile when
ïƒ demand is more inelastic

ïƒ there are more frequent changes in the supply of that good

Chapter 4: Elasticity

e.g.4.16 Expenditure Beckham

- Why does Beckham earn such an attractive income when compared to any soccer player?
- Does he have a high or low price elasticity of supply of his services?

His skills as a soccer player is a unique and essential inputs, an example of ultimate supply bottleneck.

Chapter 4: Elasticity

Example 4.17 Expenditure So why are the fares so different?

If you start in Kansas City and you fly to Honolulu round-trip, the fare is a lot lower than if you start the same trip in Honolulu and fly to Kansas City round-trip. Passengers travel on same planes, consuming the same fuel, the same in-flight amenities, and so on. So why are the fares so different?

By Karen Hittle, a student of Robert Frank.

Chapter 4: Elasticity

Example 4.17 Expenditure So why are the fares so different?

- If you are starting in Kansas City and going to Honolulu, you are probably going on vacation. You could go lots of different places. You could go to Florida, to Barbados, to Cancun. Because vacationers have many destinationsto choose from, airlines must compete fiercely for their business. Given economies of scale inherent in larger aircraft, carriers have a strong incentive to fill additional seats by targeting lower prices to the people who are more sensitive to price â€“ vacationers.

Chapter 4: Elasticity

Example 4.17 Expenditure So why are the fares so different?

- But if you are starting in Honolulu on a trip to Kansas City, you are probably not a vacationer. More likely, you either have business or family reasons for traveling. So you are probably not shopping for a destination if you are going to Kansas City.
- Travelers of which destination has a higher price elasticity of demand?

Chapter 4: Elasticity

e.g 4.18--- lifting the price ceiling Expenditure

- when a Price Ceiling is lifted, the market equilibrium quantity and price should be restored eventually.
- Price should increaseïƒ but, how much?

P

D

S

Because supply is upward sloping,

â†‘P â†’ â†‘ TR

Price Ceiling

Chapter 4: Elasticity

Q

e.g 4.18--- lifting the price ceiling Expenditure

Relative inelastic

P

D

S

increase in price that occur AFTER abolishing price control is smaller when

The price elasticity of demand is elastic.

Pe

Price Ceiling

Relative elastic

Q

Chapter 4: Elasticity

End of Expenditure

Chapter

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